Problem: Express this product in scientific notation: $(9.00\times 10^{-1})\times (9.00\times 10^{4})$
Answer: Start by collecting like terms together. $= (9.00\times 9.00) \times (10^{-1}\times 10^{4})$ When multiplying exponents with the same base, add the powers together. $= 81.0 \times 10^{-1\,+\,4}$ $= 81.0 \times 10^{3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $81.0$ is the same as $8.100 \times 10$ $ = {8.100 \times 10} \times 10^{3} $ $= 8.100\times 10^{4}$